Improving Stellar and Planetary Parameters of Transiting Planet Systems: The Case of TrES-2

We report on a spectroscopic determination of the atmospheric parameters and chemical abundance of the parent star of the recently discovered transiting planet {TrES-2}. A detailed LTE analysis of a set of \ion{Fe}{1} and \ion{Fe}{2} lines from our Keck spectra yields $T_\mathrm{eff} = 5850\pm 50$ K, $\log g = 4.4\pm 0.1$, and [Fe/H] $= -0.15\pm 0.10$. Several independent checks (e.g., additional spectroscopy, line-depth ratios) confirm the reliability of our spectroscopic $T_\mathrm{eff}$ estimate. The mass and radius of the star, needed to determine the properties of the planet, are traditionally inferred by comparison with stellar evolution models using $T_\mathrm{eff}$ and some measure of the stellar luminosity, such as the spectroscopic surface gravity (when a trigonometric parallax is unavailable, as in this case). We apply here a new method in which we use instead of $\log g$ the normalized separation $a/R_\star$ (related to the stellar density), which can be determined directly from the light curves of transiting planets with much greater precision. With the $a/R_\star$ value from the light curve analysis of Holman et al. \citeyearpar{holman07b} and our $T_\mathrm{eff}$ estimate we obtain $M_\star = 0.980\pm0.062 M_\odot$ and $R_\star = 1.000_{-0.033}^{+0.036} R_\odot$, and an evolutionary age of $5.1^{+2.7}_{-2.3}$ Gyr, in good agreement with other constraints based on the strength of the emission in the \ion{Ca}{2} H & K line cores, the Lithium abundance, and rotation. The new stellar parameters yield improved values for the planetary mass and radius of $M_p = 1.198 \pm 0.053 M_\mathrm{Jup}$ and $R_p = 1.220^{+0.045}_{-0.042} R_\mathrm{Jup}$, confirming that {TrES-2} is the most massive among the currently known nearby ($d\lesssim 300$ pc) transiting hot Jupiters. [Abridged]